Spin is a form of angular momentum, and the TOTAL angular momentum is conserved. However, spin itself can potentially be converted into orbital angular momentum, since only the TOTAL a.m. must be conserved. This is similar to the same way that potential energy can be converted into kinetic energy in classical mechanics.

There is no classical analogy to spin, so there is no easy way to visualize it like orbital angular momentum. The conservation of total a.m. follows from the isotropy of space (everything looks the same in all directions). This follows from something called "Noether's Theorem" which states (roughly) that a conservation law is always accompanied by a symmetry. So that's where the "postulate" comes from - we assume isotropy (a good assumption in nature) and that gives us conservation of a.m.

One should remember that in QM the quantities usually don't have precise values. The conservation laws must be re-interpreted as conservation of the expectation values.

However, when you read about experiments where it is said that some spin must be up and some spin down, because of the conservation of angular momentum, try to find information about the phenomenon of entanglement too, and how it is related to these experiments!

I remember being confused myself with these things, because entanglement was not being mentioned, and only the conservation laws were.

Spin is a form of angular momentum, and the TOTAL angular momentum is conserved. However, spin itself can potentially be converted into orbital angular momentum, since only the TOTAL a.m. must be conserved. This is similar to the same way that potential energy can be converted into kinetic energy in classical mechanics.

But then you have to postulate that the so called "total momentum" is conserved and spin is part of it. You wouldn't be able to derive it from lower principles.

Staff: Mentor

Note that we have experimental evidence that the microscopic intrinsic "spin" angular momentum of electrons must be taken together with the macroscopic angular momentum of an object, in conservation of total angular momentum, in the Einstein-deHaas effect.

Briefly, you align the spins of the electrons in a metal object by magnetizing it, and set the object so it is macroscopically at rest (not rotating). Even though the object is at rest, it has a net angular momentum in one direction because of the spins. Then you flip the spins, I think by using electromagnetic radiation with just the right photon energy to induce a transition between the two spin states. The spin angular momentum is now in the opposite direction, and the object starts to rotate macroscopically in the same direction that the spins were originally oriented, in order to maintain the same total angular momentum.

This is analogous to the classical angular momentum demonstration with a person sitting on a turntable and holding a bicycle wheel whose plane is horizontal. The wheel is initially spinning clockwise and the person is stationary on the turntable. When the person turns the wheel over so it is now spinning counterclockwise, he and the turntable start to rotate clockwise to maintain the same total angular momentum.

The conservation of the total angular momentum, including spin pops out of the Dirac-Equation. Spin is a relativistic effect so you need a relativistic equation to derive the conservation of total a.m. including spin from first principles.

Although spin is usually thought of as arising from the relativistic Dirac equation, on page 967 of Cohen-Tannoudji there is a footnote "This does not mean that spin has a purely relativistic origin: it can be deduced from the structure of the non-relativistic transformation group (the Galilean group)." However he gives no references. There is an article on Wilipedia 'Representation theory of the Galilean group' (also without references) that just hints at the physics. Does anybody know of any references?

Note that we have experimental evidence that the microscopic intrinsic "spin" angular momentum of electrons must be taken together with the macroscopic angular momentum of an object, in conservation of total angular momentum, in the Einstein-deHaas effect.

Ok. However that experiment doesn't exactly prove that electrons have an intrinsic angular momentum (spin), but that if it has, it must be correlated with its magnetic moment.